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May 3rd, 2010, 11:04 AM  #1 
Newbie Joined: Mar 2010 Posts: 13 Thanks: 0  Circle in an angle
Hello, given is a triangle ABC. A circle with center D is tangent to BC, AB and AC at points that lie outside the given triangle. Show that AD passes through the circumcircle of triangle BCD. I have no idea how to attempt this. Thanks for help. 
May 3rd, 2010, 01:24 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,757 Thanks: 2138 
The wording "through the circumcircle" should have been "through the circumcentre". The circumcircle of triangle BCD passes through the incentre, I, of triangle ABC, has ID as a diameter, and the midpoint of ID as its centre, which therefore lies on AD.


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